Specialization traits of nested struct

I have a template struct with a nested template struct.

template <int F>
struct foo
{
    template <int B>
    struct bar {
        static constexpr int f = F;
        static constexpr int b = B;
    };
 };

I want to create a trait like

template <class>
struct is_foo_bar : std::false_type { };

template <int F, int B>
struct is_foo_bar< foo<F>::bar<B> > : std::true_type { };

static_assert(is_foo_bar< foo<1>::bar<2> >::value);

This gives an error:

type/value mismatch at argument 1 in template parameter list for ‘template<class> struct is_foo_bar’<br>
struct is_foo_bar<foo<F>::bar<B>> : std::true_type { };

If I take bar out like

template <int F, int B>
struct foo_bar {
    static constexpr int f = F;
    static constexpr int b = B;
};

template <int F>
struct foo
{
    template <int B>
    using bar = foo_bar<F, B>;
};

template <class>
struct is_foo_bar : std::false_type { };

template <int F, int B>
struct is_foo_bar< foo_bar<F, B> > : std::true_type { };

static_assert(is_foo_bar< foo<1>::bar<2> >::value);

... it works. But this is not the way I want it to be. What I'm missing in code where bar declaration is in foo?